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Page 1: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Dynamical Fermion Simulations:

A Critical Status Report

Karl Jansen

• Lattice actions(an over-critical account)

• Performance comparison

• Systematics

continuum limit scaling nite size eects chiral perturbation theory renormalization eects of strange quark mixed action

• Conclusion

Page 2: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Welcome to the lattice and its dangerous animals

1

Page 3: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Bem-vindos `a rede e seus animals perigososÄîáðî ïîæàëîâàòü â òåîðèþ êàëèáðîâî÷íûõ ïîëåé íà ðåø¼òêàõ... Èâ ìèð å¼ îïàñíûõ æèâîòíûõ!

1

Bienvenidos a la Red y sus peligrosos animales

Dobrodosli na resetku i opasne zivotinje na njoj

Willkommen auf dem Gitter und seinen gefährlichen Tieren

Witajcie na sieci, gdzie »yj¡ niebezpieczne zwierz¦ta

Kal¸c rjate sto plègma kai ta gria jhrÐa tou

2

Page 4: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

0.15

0.10

0.05

0.001.0

0.8

0.6

0.4

0.2

0.0

600500

400300

200100

mπL = 3.5

exptJLQCD(2001) Nf = 2

MILC Nf = 2 + 1

RBC-UKQCD Nf = 2 + 1

PACS-CS Nf = 2 + 1

JLQCD Nf = 2 + 1

JLQCD Nf = 2

CLS Nf = 2

CERN-ToV Nf = 2

QCDSF Nf = 2

ETMC Nf = 2

a [fm]

1/L [fm−1]mπ [MeV]

a[fm]

1/L [fm−1]

0.15

0.10

0.05

0.001.00.80.60.40.20.0

a[fm]

mπ [MeV]

0.15

0.10

0.05

0.00600500400300200100

1/L [fm−1]

mπ [MeV]

1.0

0.8

0.6

0.4

0.2

0.0600500400300200100

The parameter landscape (thanks to G. Herdoiza)

a[fm]

1/L[fm−1]MPS[MeV]

a[fm] a[fm] 1/L[fm−1]

1/L[fm−1] MPS[MeV] MPS[MeV]

3

Page 5: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Non-perturbatively improved Wilson Fermions

This is most probably the best formulation of lattice QCD!

DRAWBACK

• for full non-perturbative O(a)-improvement

→ nonperturbative operator improvement neccessary→ very demanding (e.g. PDFs, formfactors etc.)→ sometimes neglected

• mixing under renormalization

• Moderate smearing can be helpfuldoes it harm?

• No infrared regulating quark mass

4

Page 6: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Non-perturbatively improved Wilson Fermions

• No infrared regulating quark mass

however

stability through

spectral gap

(CERN)

0 10 20 30 40 50 60 70

|λ| [MeV]

mPS=360 MeV mPS=520 MeV

mq=28 MeV mq=58 MeV

smallest eigenvalue distribution with median µ and width σ

A1 A2 A3 A4 B1 B2 C1 D10.4

0.6

0.8

1

1.2

1.4

1.6

1.8

σ√ V /a median of distribution µ ≈ Zm

demanding µ ≥ 3σ

→ m ≥ 3a/Z√

V

→ mπL ≥√

3√

2aB/Z

5

Page 7: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Stability and Meta-Stability(C. Urbach, K.J.)

Wilson plaquette gauge action and Wilson fermion action

β L mPSL µ σ

5.2 16 8 0.0103 0.0013

5.3 16 4 0.0038 0.0010

hot start

mPSL > 8

µ

ρ

0.0140.0120.010.0080.0060.0040.0020

400

350

300

250

200

150

100

50

0

⇒ all criteria fulllled

6

Page 8: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Stability and Meta-Stability

cold

hot

tHMC

〈P 〉

180016001400120010008006004002000

0.55

0.54

0.53

0.52

0.51

0.5

0.49

cold

hot

tHMC

〈P 〉

120010008006004002000

0.56

0.555

0.55

0.545

0.54

0.535

0.53

0.525

0.52

→ dierent (hot and cold) starts

→ long-living metastable states at β = 5.2 and β = 5.3

→ check for metastable behaviour towards the chiral limit(Sharpe, Wu; Münster, Hofmann; Scorzato; Farchioni et.al.)

7

Page 9: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

rooted staggered fermions

This is most probably the best formulation of lattice QCD!

DRAWBACK

• rooting issue still being discussed

non-local at a > 0 ⇒ scaling law towards continuum limit? theoretical analysis (Shamir; Sharpe; Bernard, Golterman, Shamir, Sharpe; Adams) non-perturbative couplings of tastes (Creutz)

• usage of non-exact RHMD algorithm

used for large volume simulations no eect on plaquette (Toussaint) dierence: O(10−7)

(is it safe? what about e.g. correlators?) exact RHMC algorithm about factor of 2 more expensive (Gottlieb, Toussaint)

8

Page 10: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

rooted staggered fermions: two points of view

view I

• First continuum limit, then chiral limit• needs minimal pion mass

continuum ChPT: taste splitting M2PS

staggered ChPT: taste splitting . M2PS

a = 0.060fm: M2PS = (≈ 220MeV)2 ≈ 3∗ taste splitting

a = 0.125fm: M2PS = (≈ 250MeV)2 ≈ taste splitting

• Symanzik-like analysis (Bernard, Golterman, Shamir)

Dtaste = Dinv + ∆ bound: ‖D−1inv∆‖ . a/( ma2

c︸︷︷︸blocked

)

⇒ continuum limit rst

• Order of limits: studied in Schwingermodel:(Dürr, Hoelbling)

strategy seems to be working for all practical purposes→ visit MILC presentations

9

Page 11: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

rooted staggered fermions: two points of view

view II

• Explore the chiral limit at xed lattice spacingin the end we are theorists ...

• check 't Hooft vertex (Creutz)(more general: observables related to instanton physics)

• explore ε-regime with simulations and chiral perturbation theory

10

Page 12: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

maximally twisted mass fermions

This is most probably the best formulation of lattice QCD!

DRAWBACK

L = 2.8 fm mπ ∼ 300 MeVL = 2.2 fm mπ ∼ 300 MeV

mπ ∼ 450 MeV

r20((m

±

PS)2 − (m0

PS)2)

(a/r0)2

0.040.030.020.010.00

0.4

0.3

0.2

0.1

0.0

r0fPS = 0.400r0fPS = 0.375r0fPS = 0.345

r0mPS

(a/r0)2

0.060.040.020

1.30

1.20

1.10

1.00

0.90

0.80

0.70

0.60

0.50

• neutral pion becomes zero at µtm = µcrittm

• isospin breaking

observation I

charged minus neutral only charged

→ large cuto eects in neutral pion mass

11

Page 13: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

maximally twisted mass fermions

Observation II

RO = O±−O0

β aµq RO

afPS 3.90 0.004 0.04(06)4.05 0.003 −0.03(06)

amV 3.90 0.004 0.02(07)4.05 0.003 −0.10(11)

afV 3.90 0.004 −0.07(18)4.05 0.003 −0.31(29)

am∆ 3.90 0.004 0.022(29)4.05 0.003 −0.004(45)

• Isospin splittingscompatible with zerofor other (so far)considered observables

12

Page 14: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

maximally twisted mass fermions

interpretation

analysis a la Symanzik

(m0PS)

2 = m2π + a2ζ2

π +O(a2m2π, a4) , ζπ ≡ 〈π0|L6|π0〉|cont

(m±PS)

2 = m2π +O(a2m2

π, a4)

ζπ has a large contribution:

ζ2π/Λ4

QCD ∼ 25 a2Λ4QCD

size of isospin violation needs case by case study

13

Page 15: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

high (6) level stout smeared Wilson Fermions

This is most probably the best formulation of lattice QCD!

DRAWBACK

• alter short distance behaviour?

→ here: look at static action (Farchioni,Montvay, Urbach, Wagner, K.J.)

0

0.5

1

1.5

2

0 2 4 6 8 10

Ve

ffe

ctiv

e a

T / a

effective masses for R / a = 6 for different static actions

no smearing1 HYP2 smearing step6 stout smearing steps

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6 8 10

(V -

V0)

a

R / a

static potentials for different static actions

6 stout smearing steps1 HYP2 smearing step

no smearing

Veff from below no change at R/a relevant for r0

shift r0 ≈ 6.0→ r0 ≈ 4.8 why smaller?

→ compare lattice spacing from fermionic observable → in progress

14

Page 16: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

high (6) level stout smeared Wilson Fermions

• alter short distance behaviour?

→ check localization range of gauge eld interaction

0 1 2 3 4 5 6 7

|z|/a

10-6

10-5

10-4

10-3

10-2

10-1

100

||¶D(x

,y)/¶Um(x

+z)

||

a~~0.125 fma~~0.085 fma~~0.065 fm

(BMW collaboration)

→ nd exponential localization

15

Page 17: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Domain wall Fermions

This is most probably the best formulation of lattice QCD!

DRAWBACK

• Domain Wall Fermions with NS <∞ break chiral symmetry(as do imprecisely approximated overlap fermions)

← studied by RBC-UKQCD collaboration

• cost of improved chiral symmetry? → later

• comparison mres and mminsea

a−1 mminsea mmin

val mres

1.73 0.005 0.001 0.00315(2)

2.42 0.004 0.002 0.000665(13)

16

Page 18: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Domain wall Fermions

• Changing topology

1.9 2 2.1 2.2 2.3 2.4

β

0.0001

0.001

0.01

0.1

mre

s (L

s=3

2)

• eigenvalue density of kernel operator

ρ(0)→ 0 for β →∞

mres ∝ ρ(0)/Ls

⇒ topology change forbidden for a→ 0

• consequence of negative quark massplaquette bound

• holds true also for overlap fermions

mres(Ls) Ls xed

β

17

Page 19: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Changing topology

what about other fermions?

Schwinger model with Wilson fermions (Christian, K.J.)

-1

0

1

0 100 200 300 400 500

Monte-Carlo Time

Topolo

gic

alC

harge

β = 5

-1

0

1β = 6

-1

0

1β = 10

diculty to change topology in principle problem for everybody→ think about algorithms

18

Page 20: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

overlap fermions

This is most probably the best formulation of lattice QCD!

Nigel Cundy Topology with dynamical overlap fermions

Summary

• Dynamical overlap fermions are difficult

• Correctly sampling topological sectors with dynamical overlapfermions is even more difficult

• But it is possible

• And with luck, I will have some physics to share some time inthe next century

Trento, May 2008 29/29

• However, there are simulations: 83 · 16see also (DeGrand, Schäfer)

• what about the Mandula concern?

2.5

3

3.5

4

4.5

5

5.5

6

0.02 0.025 0.03 0.035 0.04 0.045 0.05 0.055χ

t

mq

χtop

19

Page 21: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

overlap fermions in xed topology

This is most probably the best formulation of lattice QCD!

• eects of xing topology topological nite size eects (Brower et.al., Aoki et.al) algorithmic ergodocity loss of clustering properties• worth the eort? → main motivation: ε-regime

xed point action(P. Hasenfratz, Hierl, Maillart, Niedermayer, A. Schäfer, Weiermann, Weingart)

Wilson action (A. Hasenfratz, Homan, S. Schäfer) twisted mass action (Nube, Shindler, Urbach, Wenger, K.J.)

⇐ formulae in ChPT available summing over all topologies

• Wilson determinant and O(a) eects?

• τint,Ninv∝ O(100); Q independent?

• continuum form of chiral Lagrangian butbreaking of Lorentz invariance

20

Page 22: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Other Collaborations/Fermions

These are for sure ...

• Flic fermions (CSSM)

• Chirally improved fermions (BGR collaboration)

• Fixed point action (Bern group)

• Stout smeared Wilson (Hasenfratz, Homann, Schäfer)

Disclaimer: Don't forget, I have been over-critical here and played devil's advocate!

In general, I think, we are doing very well

21

Page 23: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Cost of simulations

cost formula

Cop = k(20 MeV

m

)cm (L

3 fm

)cL(0.1 fm

a

)ca Tflops× years

m renormalized quark mass at 2GeV

(sorry for shoehorning you to this form ...)

action k cm cL ca

Wilson 0.3 1 5 6(DDHMC)

staggered 0.016 1 4 4(RHMC)

tmQCD 0.8− 2.1 2 5 6(MTMHMC)

k, ca, cm, cL : large uncertainties

not to be taken as denite

e.g. ca not conrmed by ETMC data(scaling in a much weaker)

22

Page 24: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Updated Berlin Wall plot

L = 2.1fm a = 0.087fm, MPSL = 3.51000 independent congurations

tremenduous algorithmic improvementfolded with machine capacities outperforming Moore's law⇒ realistic simulations

23

Page 25: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

It's universality

Example of the Schwinger model(N. Christian, K. Nagai, B. Pollakowski, K.J.)

OverlapHypercube

1

β

β

0.88

0.86

0.84

0.82

0.80

0.78

0.76

0.74

10.80.60.40.20

Twisted massWilson

1

β

β

1 0.8 0.6 0.4 0.2 0

0.88

0.86

0.84

0.82

0.80

0.78

0.76

0.74

• mquark

√β xed

• observe a2 scaling

• universality of continuum limit

• ≈ 10% scaling violation

= a2

24

Page 26: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Continuum limit scaling(Urbach, K.J.)

• use r0 but consider r0 as scaling variable not as physical quantity

• r0 better than using the scale a−1

• r0 extrapolated to the physical point

• x r0MPS = 0.8, 1.0, 1.2

• consider r0fPS and r0Mnucleon

• nite size corrections are taken into account (fPS,MPS)

note: fPS does not need renormalization for overlap, twisted mass and staggered fermions

25

Page 27: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Continuum limit scaling: nucleon mass

LHP nf = 2 + 1PACS-CS nf = 2 + 1

JLQCD nf = 2QCDSF-UKQCD nf = 2

RBC-UKQCD nf = 2 + 1MILC, nf = 2 + 1

ETMC, nf = 2

(r0mPS)2

r0m

N

43.532.521.510.50

4.5

4

3.5

3

2.5

2

1.5

• the nucleon mass revisited

only smallest lattice spacing

→ no obvious discrepancy

→ eects of scale setting

26

Page 28: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

LHPC nf = 2 + 1 mixedJLQCD nf = 2

RBC-UKQCD nf = 2 + 1MILC nf = 2 + 1

ETMC nf = 2

r0mPS = 1.2

r0mPS = 1.0

r0mPS = 0.8

(a/r0)2

r 0m

N

0.120.10.080.060.040.020

3.4

3.2

3

2.8

2.6

2.4

2.2

2

QCDSF nf = 2PACS-CS nf = 2 + 1

ETMC nf = 2

r0mPS = 1.2

r0mPS = 1.0

r0mPS = 0.8

(a/r0)2

r 0m

N

0.120.10.080.060.040.020

3.4

3.2

3

2.8

2.6

2.4

2.2

2

Continuum limit scaling: nucleon mass

staggered, DW, overlap Wilson fermions only

→ nd overall consistency

→ eventually combined continuum limit possible

27

Page 29: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Continuum limit scaling: fPS

JLQCD nf = 2CERN nf = 2

QCDSF-UKQCD nf = 2RBC-UKQCD nf = 2 + 1

MILC, nf = 2 + 1ETMC, nf = 2

data not FS corrected!

(r0mPS)2

r 0f P

S

32.521.510.50

0.5

0.45

0.4

0.35

0.3

0.25

0.2

smallest lattice spacing only

no signs of common scaling

28

Page 30: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Continuum limit scaling: fPS

JLQCD nf = 2CERN nf = 2

QCDSF-UKQCD nf = 2RBC-UKQCD nf = 2 + 1

MILC, nf = 2 + 1ETMC, nf = 2

data not FS corrected!

(mPS/mPS,ref)2

f PS/f

PS,r

ef

32.521.510.50

1.3

1.2

1.1

1

0.9

0.8

0.7

0.6JLQCD nf = 2

MILC nf = 2 + 1ETMC nf = 2

r0mPS = 1.2

r0mPS = 1.0

r0mPS = 0.8

(a/r0)2

r 0f P

S

0.120.10.080.060.040.020

0.45

0.4

0.35

0.3

0.25

FPS normalized to reference point only formulations with ZA = 1

29

Page 31: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Continuum limit scaling: fPS

possible sources of mismatch

• non-perturbative renormalization factor ZA

• value for r0

varies from r0 = 0.45− 0.5fmvaries in time ...

• nite size eects

• Nf versus Nf = 2 + 1

⇒ need to understand this!

30

Page 32: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Do we need non-perturbative renormalization?

• strange quark mass (tm-example, arXiv:0709.4574)

ZRI−MOMP (1/a) = 0.39(1)(2) ← non-perturbative RI-MOM method

ZBPTP (1/a) ' 0.57(5) ← one-loop boosted perturbation theory

mMSq (2GeV)MeV perturbative non-perturbative

mud 2.63± 0.08± 0.36 3.85± 0.12± 0.4mud (PACS-CS) 2.53± 0.05

ms 72± 2± 9 105± 3± 9ms (PACS-CS) 72.7± 0.8

31

Page 33: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Do we need non-perturbative renormalization?

• want massless renormalization scheme

Nf = 2RI-MOM: chiral extrapolationSF: direct at mquark = 0

Nf = 2 + 1RI-MOM: presently, only light quarks chirally extrapolated, strange xed(RBC-UKQCD) estimates systematic eectsSF: rst simulations (talk by Taniguchi)

• renormalization needs dedicated runs with Nf = 3 mass degenerate quarks

• appetizer: this checks simultaneously SU(3) ChPTMILC is planning to perform such runs

32

Page 34: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Eects of dynamical strange?

strange quark mass compilation (compiled by V. Lubicz)

40 60 80 100 120 140 160 180 200ms (2 GeV) [MeV]

CP-PACS 01

JLQCD 02

ALPHA 05

SPQcdR 05

QCDSF-UKQCD 04-06

ETMC 07

HPQCD-MILC-UKQCD 04-07

CP-PACS-JLQCD 07

PDG 06 Average

(W-Clov, a-->0, PT)

(W-Clov, a=0.09 fm, PT)

(W-Clov, a=0.07 fm, SF)

(Wilson, a=0.06 fm, RI-MOM)

(W-Clov, a-->0, RI-MOM)

(TM, a=0.09 fm, RI-MOM)

(KS, a-->0, PT)

(W-Clov, a-->0, PT)

(Lattice only)

RBC 07(DWF, a=0.12 fm, RI-MOM)

(DWF, a=0.11 fm, RI-MOM)RBC-UKQCD 08

PACS-CS 07(W-Clov, a=0.09, PT)

Nf=2

Nf=2+1

→ no obvious eect of dynamical strange quark

33

Page 35: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

MILCETMC

(a/r0)2

r0m

Ω

0.080.060.040.020

5

4.8

4.6

4.4

4.2

4

3.8

3.6

Eects of dynamical strange?

take the Ω(sss− baryon)-mass: chiral limit, no strong decay

• r0MPS xed

→ no obvious eect (however, large errors)

34

Page 36: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Mixed action

overlap on twisted mass sea: match MPS (Garron, Scorzato)

→ nd at matching point: fPS(tm) = 0.0646(4)

fPS(overlap) = 0.054(3)

domain wall on rooted staggered fermions: match MPS (LHP collaboration)

→ nd at matching point: Mnucleon(staggered) = 0.723(6)

Mnucleon(domainwall) = 0.696(7)

check cuto eects in mixed action calculations

→ chiral perturbation theory analysis(Bär, Rupak, Shoresh; Golterman, Izubuchi, Shamir)

35

Page 37: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

where to apply 1-loop and 2-loop chiral perturbation theory?

• SU(2) χPT

β = 4.05

β = 3.90

NNLO χPT

NLO χPT

r0µRr 0

fP

S

0.20.150.10.050

0.45

0.40

0.35

0.30

0.25

(JLQCD) (ETMC)

x = 2B0mq

(4πf)2x = 2B0mq

(4πf)2

x = ( mπ4πf )2 nite size corrected

ξ = ( mπ4πfπ

)2 ⇒ NLO for MPS . 450MeV valid (?)

36

Page 38: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

NNLO needed?

scalar radius:

log in

log may

become signiÞcant beyond the region of lattice data.

← JLQCD

〈r2〉πV = 1(4πfπ)2

[ln m2

πµ2 + 12(4π2)l9

]also seen byETMC

〈r2〉πcharge = 1(4πfπ)2

[ln Λ2

62Bm − 1

]

37

Page 39: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Nf = 2 + 1 avours

• SU(3) chiral perturbation theoryexample: (PACS-CS)

0 0.01 0.02 0.03

mud

AWI

0.05

0.06

0.07

0.08

0.09

0.10

κs=0.13640

κs=0.13660

chptchpt@ph

0 0.01 0.02 0.03

mud

AWI

0.06

0.07

0.08

0.09

0.10

κs=0.13640

κs=0.13660

chptchpt@ph

fK

⇒ SU(3) not a good descriptionalso concluded by other groups

38

Page 40: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Nf = 2 + 1 avours

• SU(2) chiral perturbation theory partially quenched chiral perturbation theory ts work for mquark . 0.01 (MPS . 450 MeV)

(0.06 fm) results are to the continuum extrapolation.

0.08

0.09

0.1

0.11

0 0.01 0.02 0.03 0.04mx

my = 0.04fit: mx ≤ 0.01

fxy

ml=0.005ml=0.01

mx=mlmx=ml=mud

(MILC) (RBC-UKQCD)

rooted staggered perturbation theory kaon ChPTadd NNLO anayltic terms issue of uncorrelated ts(only sea quark data shown)

39

Page 41: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Nf = 2 + 1 avours

staggered data at a = 0.06fm seem to be close to continuum ⇒

• SU(2) 2-loop continuum chiral perturbation theory(rSχPT is not catching up to this order)

→ extend t range

(C. Bernard, MILC)

40

Page 42: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

A comparison

B f l3 l4

SU(2)×SU(2) 2.414(61) 0.0665(21) 3.13(33) 4.43(14)

SU(3)×SU(3) 2.457(78) 0.0661(18) 2.87(28) 4.10(05)

MILC (Nf = 2 + 1) 0.6(1.2) 3.9(5)

MILC, pure NLO 2.85(07) –

ETMC (Nf = 2) 3.44(08)(35) 4.61(04)(11)

CERN (Nf = 2) 3.0(5) –

phenom. 2.9(2.4) 4.4(0.2)

E. Scholz, RBC-UKQCD

41

Page 43: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Summary chiral perturbation theory

Nf = 2

• SU(2) χPT seems to work for MPS . 450MeV

2-loop eects seem to be important for pion radii constraining ts, add more observables,

go down to 200MeVpion masses

Nf = 2 + 1

• SU(3) χPT not working for kaon sector

to explore SU(3) χPT → need Nf = 3 simulations(seems to be request from χPTheorists (Colangelo) )

SU(2) χPT including lattice artefacts works for MPS . 450MeV continuum SU(2) χPT at NNLO

nal check: χPT after continuum extrapolation

understand scaling

42

Page 44: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Topological susceptibility

→ χtopo shows right behaviour in chiral limit

→ χtopo particularly important for xed topology

(RBC-UKQCD) (MILC)

0 0.05 0.1 0.15 0.2 0.25r0 (m

u + m

res)

0

0.01

0.02

0.03

0.04

0.05

Topolo

gic

al susceptibili

ty, r 0

16332, L

s=16

24364, L

s=16

Iwasaki gauge action, a~0.13 fm

Curve is based on measured and 43

Page 45: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

η2 mass

• η2 (Nf = 2) analogue of η′ (Nf = 2 + 1)

DWF r0/a = 4.28CP-PACS r0/a = 4.49UKQCD r0/a = 5.04UKQCD r0/a = 5.32

ETMC r0/a = 6.61ETMC r0/a = 5.22 L = 32ETMC r0/a = 5.22 L = 24

(r0mπ)2

r 0m

η

3210

3

2

1

0

(ETMC)

→ reach small pion masses

→ conrm mass of η2 ≈ 700MeV

44

Page 46: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Finite size eects

Comparison of data at several volumes to :

rSχPT CDH (Colangelo, Dürr, Haefeli)

observed “boosted” 1-loop rS PTquantity

1.4(2)% 1.6(2)% 1.1%0.4(3) % 0.4(3) % 0.3%

% % %% % %

observ. MPSL meas. [%] CDH [%]MPS 3.0 +6.2 +6.1fPS 3.0 −10.7 −10.3MPS 3.5 +1.1 +1.5fPS 3.5 −1.8 −2.9

(MILC) (ETMC)

MPSL = 4 relative deviation: RO = OL−O∞)O∞

45

Page 47: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Finite size eects from SU(3) ChPT

50 100 150 200 250 300 350 400mπ [MeV]

0.00

0.02

0.04

0.06

0.08

0.10

X=mπX=mKX=fπ

X=fK

|RX|• RX = (X(L)−X(∞))/X(∞)

• L = 3fm

(PACS-CS)

→ nite size eects small even at physical point

46

Page 48: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Dangerous nite size eects

FS corrected Corrections gA/gV in DWF

0 0.1 0.2 0.3 0.4 0.5mπ

2[GeV2]

0.7

0.8

0.9

1

1.1

1.2

1.3

Nf=2+1(2.7fm)Nf=2+1(1.8fm)Nf=2(1.9fm)experiment

gA/gV(DWF)

(QCDSF) (RBC-UKCD)

predict: L = 2.5fm, MPS = 140MeV: 20%

47

Page 49: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Some bounds for simulations

stability bound δ expansion

mπL ≥√

3√

2aB/Z

nite size eects minimal pion mass

MPSL ≥ 3.5 MPSL ≥ 3/2∗f20L2

1.+5.7/4∗π∗f20L2

48

Page 50: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Getting social

• ILDG: put congurations on the net! (talk by T. Yoshie)

• Codes: publish code (MILC (arXiv:0806.2312), Lüscher, Borici)

• Techniques: publish papers with all technical details

49

Page 51: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Challenges for dynamical simulations

• Decay of unstable particles, resonances

• Disconnected contributions

• Change of topological charge towards the continuum limit

• Blind test of data analysis

• Collaborations with non-lattice peoplee.g.: (Allison et.al., arXiv:0805.2999)

50

Page 52: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Conclusion: there is a rooting problem!

Who do we root for now?Which dynasty do we want continuing to wave its victorious ag?

• thanks to algorithmic, machine and conceptual improvements:→ after many years of preparatory work simulations are done at

Pion mass: 200MeV . MPS and even MPS = 140MeV lattice spacing: 0.05fm . a lattice size: MPS · L ≥ 3.5

• investigate more: systematics of dierent lattice formulations:fourth root, stouting, isopin breaking, autocorrelations,residual mass, topology xing, ...

• observations: scaling towards continuum limit problematic, e.g. fPS

applicability of χPT up to the strange quark questionable need massless renormalization with dynamical strange quark dangerous nite size eects, e.g. gA

mixed action may have non-negligible cuto eects

51

Page 53: Dynamical Fermion Simulations: A Critical Status Reportconferences.jlab.org/lattice2008/talks/plenary/karl_jansen.pdf · Dynamical Fermion Simulations: A Critical Status Report Karl

Conclusion: whom to root for?

• the dynasties:BMW, CLS, PACS-CS, ETMC, JLQCD, MILC, QCDSF, PACS-CS, RBC-UKQCDLet's go for all ⇒ universality will tell

0

500

1000

1500

2000

M[MeV]

p

K

r K*NLSX D

S*X*O

experiment

width

QCD

(BMW collaboration)

52


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